Archive for January, 2007

Politicians, particularly those who have worked their way to senior positions in government, are necessarily cunning, intelligent people. Many may not seem to be at first glance but the nature of the game ensures that only the cleverest, and importantly, the most ruthless, survive or get very far. Why is it then, that they say such silly things?

A pair of interesting results on the common theme of refraction, or more specifically, refractive index, have been published in the last month. The first, reported in last year’s penultimate Nature (subscription required) is a good example of a simple physical question for which an answer is still elusive. The problem is this: what is the momentum of light in media other than the vacuum?

I think questions like these are wonderful for their simplicity, but on the other hand it’s embarrassing to realise modern physics can’t answer them. To see why this is the case, let’s examine some possible responses. We can take as given that light slows down in a non-vacuous media of refractive index n, to have speed c/n. There are two ways to proceed, the first due to Minkowski1, the second to Abraham2.

The wave equation inside a medium of index n is λν = c/n. The Planck relation for light is E = hν, so that E(λ/h) = n/c, and as the de Broglie momentum is p = h/λ, the result is simple and even requires no Greek letters: p = (nE)/c.

The postulates of relativity necessitate, after some thought, that E=mc2. While it isn’t sensible to talk of light having mass per se, no-one would frown if you wrote out the momentum as ‘mass’ times velocity, and this is just what Abraham did: p = (E/c2)(c/n) = E/nc.

Oh no! The two expressions differ by a factor of n2. They are only equivalent for the vacuum case, which is no help at all. For everyday transparent substances, we expect n to be just a bit larger than 1, but enough so n2 is a measurable factor. The arbiter is of course experiment, and these have been carried out. Minkowski predicts that the momentum goes up, Abraham that it goes down. Place your bets now.